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Variable Magnetic Permeance

Purpose

Variable permeance controlled by external signal

Library

Magnetic

Description

pict

This component provides a magnetic flux path with a variable permeance. The component is used to model non-linear magnetic material properties such as saturation and hysteresis. The permeance is determined by the signal fed into the input of the component. The flux-rate through a variable permeance P(t)   is governed by the equation:

    d             dF   d
P = --(P ⋅F) = P ⋅---+ --P ⋅F
    dt            dt   dt

Since F   is the state variable the equation above must be solved for dFdt-  . The control signal must provide the values of P(t)  , dP(t)
dt   and P   as a vector. It is the responsibility of the user to provide the appropriate signals.

Modeling non-linear material properties

When specifying the characteristic of a non-linear permeance, we need to distinguish carefully between the total permeance P  (F) = P∕F
 tot   and the differential permeance P  (F ) = dP∕dF
 diff  .

If the total permeance Ptot(F )   is known the flux-rate P   through a time-varying permeance is calculated as:

P  =   dP-
       dt
   =   d-(P   ⋅F)
       dt  tot
   =   Ptot ⋅ dF-+ dPtot⋅F
            dt     dt
   =   Ptot ⋅ dF-+ dPtot⋅ dF ⋅F
       (    dt    dF  ) dt
   =    Ptot + dPtot⋅F  ⋅ dF
               dF        dt

In this case, the control signal for the variable permeance component is:

⌊  P(t)  ⌋  ⌊        d--      ⌋
⌈ -d     ⌉ = ⌈ Ptot + dF Ptot ⋅F ⌉
  dtP(t)             0
   P(t)            Ptot ⋅F

In most cases, however, the differential permeance P   (F )
 diff   is provided to characterize magnetic saturation and hysteresis. With

       dP-
P   =   dt
       dP-  dF-
    =  dF ⋅ dt
    =  P   ⋅ dF
        diff  dt

the control signal is

⌊  P(t)  ⌋   ⌊  P     ⌋
⌈ -dP(t) ⌉ = ⌈   d0iff  ⌉
  dtP(t)        P   ⋅F
                tot

Parameters

Initial MMF
Magneto-motive force at simulation start, in ampere-turns (A).

Probe Signals

MMF
The magneto-motive force measured from the marked to the unmarked terminal, in ampere-turns (A).
Flux
The magnetic flux flowing through the component, in webers (Wb). A flux entering at the marked terminal is counted as positive.